I'm not vick or serge, but I'll give my tourist input.
The spy museum was fun and a lot less kid oriented than I thought it might be. My dad and brother didn't really want to go for that very reason, but they ended up enjoying it very much, and it's not far from the white house and the capitol.
http://www.spymuseum.org
Also, I would highly recommend getting in touch with a representative of Georgia about scheduling a tour of the capitol building, the sooner the better. They will have their interns give you a pretty in-depth tour for free and will give you some Georgia related info during the tour. You can still take a regular tour, same day without contacting anyone, though. Most of the interns are aspiring lawyers and such, very insightful.
As has been said before, no car is needed, it would probably slow you down. Their subway system is pretty modern (get the day pass).
And of course don't forget you are going to have your bags checked and go through a metal detector at every government building, so leave the steel-mesh underwear at the hotel.
Serge recommended an art museum that was unfortunately closed when I went (not sure if it was the national gallery of art or a smaller one, it was a while ago). I put in an email to my dads cousin about a casual outdoor 40th story restaurant we went to that overlooks the back of the whitehouse.
My biggest regret was not going around and taking more nighttime pictures of buildings and monuments. Hopefully something in here is helpful, we really didn't do too much out of the tourist norm.
Hope you enjoy the trip, I had a blast when I went. It's history class come alive, but with hilarious "F.B.I. Agent" t-shirts for sale.